return sample;
}
-/* Given a basic set "bset" and an affine function "f"/"denom",
- * check if bset is bounded and non-empty and if so, return the minimal
- * and maximal value attained by the affine function in "min" and "max".
- * The minimal value is rounded up to the nearest integer, while the
- * maximal value is rounded down.
- * The return value indicates whether the set was empty or unbounded.
- *
- * If we happen to find an integer point while looking for the minimal
- * or maximal value, then we record that value in "bset" and return early.
- */
-static enum isl_lp_result basic_set_range(struct isl_basic_set *bset,
- isl_int *f, isl_int denom, isl_int *min, isl_int *max)
-{
- unsigned dim;
- struct isl_tab *tab;
- enum isl_lp_result res;
-
- if (!bset)
- return isl_lp_error;
- if (isl_basic_set_fast_is_empty(bset))
- return isl_lp_empty;
-
- tab = isl_tab_from_basic_set(bset);
- res = isl_tab_min(tab, f, denom, min, NULL, 0);
- if (res != isl_lp_ok)
- goto done;
-
- if (isl_tab_sample_is_integer(tab)) {
- isl_vec_free(bset->sample);
- bset->sample = isl_tab_get_sample_value(tab);
- if (!bset->sample)
- goto error;
- isl_int_set(*max, *min);
- goto done;
- }
-
- dim = isl_basic_set_total_dim(bset);
- isl_seq_neg(f, f, 1 + dim);
- res = isl_tab_min(tab, f, denom, max, NULL, 0);
- isl_seq_neg(f, f, 1 + dim);
- isl_int_neg(*max, *max);
-
- if (isl_tab_sample_is_integer(tab)) {
- isl_vec_free(bset->sample);
- bset->sample = isl_tab_get_sample_value(tab);
- if (!bset->sample)
- goto error;
- }
-
-done:
- isl_tab_free(tab);
- return res;
-error:
- isl_tab_free(tab);
- return isl_lp_error;
-}
-
-/* Perform a basis reduction on "bset" and return the inverse of
- * the new basis, i.e., an affine mapping from the new coordinates to the old,
- * in *T.
- */
-static struct isl_basic_set *basic_set_reduced(struct isl_basic_set *bset,
- struct isl_mat **T)
-{
- unsigned gbr_only_first;
-
- *T = NULL;
- if (!bset)
- return NULL;
-
- gbr_only_first = bset->ctx->gbr_only_first;
- bset->ctx->gbr_only_first = bset->ctx->gbr == ISL_GBR_ALWAYS;
- *T = isl_basic_set_reduced_basis(bset);
- bset->ctx->gbr_only_first = gbr_only_first;
-
- *T = isl_mat_right_inverse(*T);
-
- bset = isl_basic_set_preimage(bset, isl_mat_copy(*T));
- if (!bset)
- goto error;
-
- return bset;
-error:
- isl_mat_free(*T);
- *T = NULL;
- return NULL;
-}
-
-static struct isl_vec *sample_bounded(struct isl_basic_set *bset);
-
-/* Given a basic set "bset" whose first coordinate ranges between
- * "min" and "max", step through all values from min to max, until
- * the slice of bset with the first coordinate fixed to one of these
- * values contains an integer point. If such a point is found, return it.
- * If none of the slices contains any integer point, then bset itself
- * doesn't contain any integer point and an empty sample is returned.
- */
-static struct isl_vec *sample_scan(struct isl_basic_set *bset,
- isl_int min, isl_int max)
-{
- unsigned total;
- struct isl_basic_set *slice = NULL;
- struct isl_vec *sample = NULL;
- isl_int tmp;
-
- total = isl_basic_set_total_dim(bset);
-
- isl_int_init(tmp);
- for (isl_int_set(tmp, min); isl_int_le(tmp, max);
- isl_int_add_ui(tmp, tmp, 1)) {
- int k;
-
- slice = isl_basic_set_copy(bset);
- slice = isl_basic_set_cow(slice);
- slice = isl_basic_set_extend_constraints(slice, 1, 0);
- k = isl_basic_set_alloc_equality(slice);
- if (k < 0)
- goto error;
- isl_int_set(slice->eq[k][0], tmp);
- isl_int_set_si(slice->eq[k][1], -1);
- isl_seq_clr(slice->eq[k] + 2, total - 1);
- slice = isl_basic_set_simplify(slice);
- sample = sample_bounded(slice);
- slice = NULL;
- if (!sample)
- goto error;
- if (sample->size > 0)
- break;
- isl_vec_free(sample);
- sample = NULL;
- }
- if (!sample)
- sample = empty_sample(bset);
- else
- isl_basic_set_free(bset);
- isl_int_clear(tmp);
- return sample;
-error:
- isl_basic_set_free(bset);
- isl_basic_set_free(slice);
- isl_int_clear(tmp);
- return NULL;
-}
-
/* Given a basic set that is known to be bounded, find and return
* an integer point in the basic set, if there is any.
*
- * After handling some trivial cases, we check the range of the
- * first coordinate. If this coordinate can only attain one integer
- * value, we are happy. Otherwise, we perform basis reduction and
- * determine the new range.
+ * After handling some trivial cases, we perform a depth first search
+ * for an integer point, by scanning all possible values in the range
+ * attained by a basis vector.
*
- * Then we step through all possible values in the range in sample_scan.
+ * The search is implemented iteratively. "level" identifies the current
+ * basis vector. "init" is true if we want the first value at the current
+ * level and false if we want the next value.
*
- * If any basis reduction was performed, the sample value found, if any,
- * is transformed back to the original space.
+ * The initial basis is the identity matrix. If the range in some direction
+ * contains more than one integer value, we perform basis reduction based
+ * on the value of ctx->gbr
+ * - ISL_GBR_NEVER: never perform basis reduction
+ * - ISL_GBR_ONCE: only perform basis reduction the first
+ * time such a range is encountered
+ * - ISL_GBR_ALWAYS: always perform basis reduction when
+ * such a range is encountered
+ *
+ * When ctx->gbr is set to ISL_GBR_ALWAYS, then we allow the basis
+ * reduction computation to return early. That is, as soon as it
+ * finds a reasonable first direction.
*/
static struct isl_vec *sample_bounded(struct isl_basic_set *bset)
{
unsigned gbr;
struct isl_ctx *ctx;
struct isl_vec *sample;
- struct isl_vec *obj = NULL;
- struct isl_mat *T = NULL;
- isl_int min, max;
+ struct isl_vec *min;
+ struct isl_vec *max;
enum isl_lp_result res;
+ int level;
+ int init;
+ int reduced;
+ struct isl_tab_undo **snap;
+ struct isl_tab *tab = NULL;
if (!bset)
return NULL;
ctx = bset->ctx;
gbr = ctx->gbr;
- isl_int_init(min);
- isl_int_init(max);
- obj = isl_vec_alloc(bset->ctx, 1 + dim);
- if (!obj)
- goto error;
- isl_seq_clr(obj->el, 1+ dim);
- isl_int_set_si(obj->el[1], 1);
+ min = isl_vec_alloc(bset->ctx, dim);
+ max = isl_vec_alloc(bset->ctx, dim);
+ snap = isl_alloc_array(bset->ctx, struct isl_tab_undo *, dim);
- res = basic_set_range(bset, obj->el, bset->ctx->one, &min, &max);
- if (res == isl_lp_error)
+ if (!min || !max || !snap)
goto error;
- isl_assert(bset->ctx, res != isl_lp_unbounded, goto error);
- if (bset->sample) {
- sample = isl_vec_copy(bset->sample);
- isl_basic_set_free(bset);
- goto out;
- }
- if (res == isl_lp_empty || isl_int_lt(max, min)) {
- sample = empty_sample(bset);
- goto out;
- }
- if (ctx->gbr != ISL_GBR_NEVER && isl_int_ne(min, max)) {
- if (ctx->gbr == ISL_GBR_ONCE)
- ctx->gbr = ISL_GBR_NEVER;
+ tab = isl_tab_from_basic_set(bset);
+ if (!tab)
+ goto error;
- bset = basic_set_reduced(bset, &T);
- if (!bset)
- goto error;
+ tab->basis = isl_mat_identity(bset->ctx, 1 + dim);
+ if (!tab->basis)
+ goto error;
- res = basic_set_range(bset, obj->el, bset->ctx->one, &min, &max);
- if (res == isl_lp_error)
- goto error;
- isl_assert(bset->ctx, res != isl_lp_unbounded, goto error);
- if (bset->sample) {
- sample = isl_vec_copy(bset->sample);
- isl_basic_set_free(bset);
- goto out;
+ level = 0;
+ init = 1;
+ reduced = 0;
+
+ while (level >= 0) {
+ int empty = 0;
+ if (init) {
+ res = isl_tab_min(tab, tab->basis->row[1 + level],
+ bset->ctx->one, &min->el[level], NULL, 0);
+ if (res == isl_lp_empty)
+ empty = 1;
+ if (res == isl_lp_error || res == isl_lp_unbounded)
+ goto error;
+ if (!empty && isl_tab_sample_is_integer(tab))
+ break;
+ isl_seq_neg(tab->basis->row[1 + level] + 1,
+ tab->basis->row[1 + level] + 1, dim);
+ res = isl_tab_min(tab, tab->basis->row[1 + level],
+ bset->ctx->one, &max->el[level], NULL, 0);
+ isl_seq_neg(tab->basis->row[1 + level] + 1,
+ tab->basis->row[1 + level] + 1, dim);
+ isl_int_neg(max->el[level], max->el[level]);
+ if (res == isl_lp_empty)
+ empty = 1;
+ if (res == isl_lp_error || res == isl_lp_unbounded)
+ goto error;
+ if (!empty && isl_tab_sample_is_integer(tab))
+ break;
+ if (!empty && !reduced && ctx->gbr != ISL_GBR_NEVER &&
+ isl_int_lt(min->el[level], max->el[level])) {
+ unsigned gbr_only_first;
+ if (ctx->gbr == ISL_GBR_ONCE)
+ ctx->gbr = ISL_GBR_NEVER;
+ tab->n_zero = level;
+ gbr_only_first = bset->ctx->gbr_only_first;
+ bset->ctx->gbr_only_first =
+ bset->ctx->gbr == ISL_GBR_ALWAYS;
+ tab = isl_tab_compute_reduced_basis(tab);
+ bset->ctx->gbr_only_first = gbr_only_first;
+ if (!tab || !tab->basis)
+ goto error;
+ reduced = 1;
+ continue;
+ }
+ reduced = 0;
+ snap[level] = isl_tab_snap(tab);
+ } else
+ isl_int_add_ui(min->el[level], min->el[level], 1);
+
+ if (empty || isl_int_gt(min->el[level], max->el[level])) {
+ level--;
+ init = 0;
+ if (level >= 0)
+ isl_tab_rollback(tab, snap[level]);
+ continue;
}
- if (res == isl_lp_empty || isl_int_lt(max, min)) {
- sample = empty_sample(bset);
- goto out;
+ isl_int_neg(tab->basis->row[1 + level][0], min->el[level]);
+ tab = isl_tab_add_valid_eq(tab, tab->basis->row[1 + level]);
+ isl_int_set_si(tab->basis->row[1 + level][0], 0);
+ if (level < dim - 1) {
+ ++level;
+ init = 1;
+ continue;
}
+ break;
}
+ if (level >= 0) {
+ sample = isl_tab_get_sample_value(tab);
+ isl_vec_free(bset->sample);
+ bset->sample = isl_vec_copy(sample);
+ isl_basic_set_free(bset);
+ } else
+ sample = empty_sample(bset);
- sample = sample_scan(bset, min, max);
-out:
- if (T) {
- if (!sample || sample->size == 0)
- isl_mat_free(T);
- else
- sample = isl_mat_vec_product(T, sample);
- }
- isl_vec_free(obj);
- isl_int_clear(min);
- isl_int_clear(max);
+ isl_vec_free(min);
+ isl_vec_free(max);
+ free(snap);
ctx->gbr = gbr;
+ isl_tab_free(tab);
return sample;
error:
ctx->gbr = gbr;
- isl_mat_free(T);
isl_basic_set_free(bset);
- isl_vec_free(obj);
- isl_int_clear(min);
- isl_int_clear(max);
+ isl_vec_free(min);
+ isl_vec_free(max);
+ free(snap);
+ isl_tab_free(tab);
return NULL;
}
projects / platform / upstream / isl.git / commitdiff